Table of Contents
What Is Field Energy Density?
Energy density describes the amount of energy stored per unit volume in an electromagnetic field. Both electric and magnetic fields store energy in the space they occupy. This concept is essential for understanding capacitors, inductors, electromagnetic waves, and energy transmission through space.
In electromagnetic waves, the electric and magnetic energy densities are equal, and the wave carries energy at the speed of light. In static fields such as inside a capacitor or around a permanent magnet, energy density is constant and can be calculated independently for each field type.
Formulas
Where ε₀ = 8.854 × 10⁻¹² F/m is the vacuum permittivity, μ₀ = 4π × 10⁻⁷ H/m is the vacuum permeability, and εr and μr are the relative permittivity and permeability of the medium.
Comparing Fields
| Source | Typical E or B | Energy Density |
|---|---|---|
| Capacitor (1kV, 1mm gap) | 10⁶ V/m | 4.4 J/m³ |
| MRI magnet (1.5 T) | 1.5 T | 895 kJ/m³ |
| Earth's field | 50 μT | 0.001 J/m³ |
| Lightning bolt | 3×10⁶ V/m | 40 kJ/m³ |
Frequently Asked Questions
Why is magnetic energy density usually much larger?
A 1 T magnetic field stores about 400 kJ/m³, while achieving similar electric energy density requires extremely high electric fields (about 300 MV/m). This is why superconducting magnetic energy storage (SMES) systems use magnetic fields rather than electric fields for bulk energy storage.
Are E and B energy densities equal in electromagnetic waves?
Yes. In an EM wave propagating through vacuum, the electric and magnetic energy densities are exactly equal at every point in space and time. This means E/c = B for the field amplitudes. The total energy density oscillates between zero and its maximum as the wave propagates.
How is energy density used in capacitor design?
The energy stored in a capacitor equals the energy density times the volume between the plates: U = ½εE² × Ad where A is plate area and d is separation. Higher permittivity dielectrics increase energy density, allowing smaller capacitors for the same energy storage.